TSTP Solution File: GRP485-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : GRP485-1 : TPTP v8.1.0. Released v2.6.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 11:47:42 EDT 2022
% Result : Unsatisfiable 0.15s 0.38s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 5
% Syntax : Number of clauses : 48 ( 48 unt; 0 nHn; 48 RR)
% Number of literals : 48 ( 0 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),double_divide(v,identity))),double_divide(identity,identity)),w),
file('GRP485-1.p',unknown),
[] ).
cnf(2,axiom,
equal(double_divide(double_divide(u,v),identity),multiply(v,u)),
file('GRP485-1.p',unknown),
[] ).
cnf(3,axiom,
equal(double_divide(u,identity),inverse(u)),
file('GRP485-1.p',unknown),
[] ).
cnf(4,axiom,
equal(double_divide(u,inverse(u)),identity),
file('GRP485-1.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(identity,a2),a2),
file('GRP485-1.p',unknown),
[] ).
cnf(6,plain,
equal(inverse(double_divide(u,v)),multiply(v,u)),
inference(rew,[status(thm),theory(equality)],[3,2]),
[iquote('0:Rew:3.0,2.0')] ).
cnf(7,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(double_divide(u,v),w),inverse(v))),inverse(identity)),w),
inference(rew,[status(thm),theory(equality)],[3,1]),
[iquote('0:Rew:3.0,1.0,3.0,1.0')] ).
cnf(10,plain,
equal(double_divide(double_divide(u,v),multiply(v,u)),identity),
inference(spr,[status(thm),theory(equality)],[6,4]),
[iquote('0:SpR:6.0,4.0')] ).
cnf(12,plain,
equal(multiply(inverse(u),u),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[4,6]),
[iquote('0:SpR:4.0,6.0')] ).
cnf(13,plain,
equal(multiply(identity,u),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[3,6]),
[iquote('0:SpR:3.0,6.0')] ).
cnf(14,plain,
~ equal(inverse(inverse(a2)),a2),
inference(rew,[status(thm),theory(equality)],[13,5]),
[iquote('0:Rew:13.0,5.0')] ).
cnf(16,plain,
equal(multiply(multiply(u,v),double_divide(v,u)),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[6,12]),
[iquote('0:SpR:6.0,12.0')] ).
cnf(54,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),inverse(identity))),inverse(identity)),v),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(57,plain,
equal(double_divide(double_divide(u,double_divide(inverse(double_divide(u,v)),inverse(v))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[3,7]),
[iquote('0:SpR:3.0,7.0')] ).
cnf(58,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(v))),inverse(identity)),multiply(v,u)),
inference(spr,[status(thm),theory(equality)],[10,7]),
[iquote('0:SpR:10.0,7.0')] ).
cnf(60,plain,
equal(double_divide(double_divide(u,double_divide(multiply(v,u),inverse(v))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[6,57]),
[iquote('0:Rew:6.0,57.0')] ).
cnf(69,plain,
equal(double_divide(double_divide(u,multiply(v,double_divide(u,identity))),inverse(identity)),double_divide(identity,inverse(v))),
inference(spr,[status(thm),theory(equality)],[58,7]),
[iquote('0:SpR:58.0,7.0')] ).
cnf(73,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),multiply(identity,u)),
inference(spr,[status(thm),theory(equality)],[4,58]),
[iquote('0:SpR:4.0,58.0')] ).
cnf(74,plain,
equal(double_divide(inverse(u),inverse(identity)),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[3,73,13]),
[iquote('0:Rew:3.0,73.0,13.0,73.0')] ).
cnf(76,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(u))),inverse(identity)),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[3,69]),
[iquote('0:Rew:3.0,69.0')] ).
cnf(79,plain,
equal(multiply(inverse(identity),inverse(u)),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[74,6]),
[iquote('0:SpR:74.0,6.0')] ).
cnf(84,plain,
equal(double_divide(multiply(u,v),inverse(identity)),inverse(multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[6,74]),
[iquote('0:SpR:6.0,74.0')] ).
cnf(108,plain,
equal(double_divide(multiply(u,double_divide(v,identity)),inverse(u)),double_divide(double_divide(v,identity),inverse(identity))),
inference(spr,[status(thm),theory(equality)],[60,7]),
[iquote('0:SpR:60.0,7.0')] ).
cnf(116,plain,
equal(double_divide(double_divide(u,inverse(multiply(identity,u))),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[84,60]),
[iquote('0:SpR:84.0,60.0')] ).
cnf(117,plain,
equal(double_divide(double_divide(u,inverse(inverse(inverse(u)))),inverse(identity)),identity),
inference(rew,[status(thm),theory(equality)],[13,116]),
[iquote('0:Rew:13.0,116.0')] ).
cnf(120,plain,
equal(double_divide(multiply(u,inverse(v)),inverse(u)),inverse(inverse(v))),
inference(rew,[status(thm),theory(equality)],[74,108,3]),
[iquote('0:Rew:74.0,108.0,3.0,108.0')] ).
cnf(128,plain,
equal(double_divide(double_divide(u,identity),inverse(identity)),inverse(inverse(inverse(double_divide(u,identity))))),
inference(spr,[status(thm),theory(equality)],[117,7]),
[iquote('0:SpR:117.0,7.0')] ).
cnf(133,plain,
equal(inverse(inverse(inverse(inverse(u)))),inverse(inverse(u))),
inference(rew,[status(thm),theory(equality)],[74,128,3]),
[iquote('0:Rew:74.0,128.0,3.0,128.0')] ).
cnf(148,plain,
equal(double_divide(double_divide(u,double_divide(identity,inverse(inverse(v)))),inverse(identity)),multiply(inverse(inverse(inverse(v))),u)),
inference(spr,[status(thm),theory(equality)],[133,58]),
[iquote('0:SpR:133.0,58.0')] ).
cnf(155,plain,
equal(multiply(inverse(inverse(inverse(u))),v),multiply(inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[58,148]),
[iquote('0:Rew:58.0,148.0')] ).
cnf(204,plain,
equal(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(inverse(v)))),
inference(spr,[status(thm),theory(equality)],[120,6]),
[iquote('0:SpR:120.0,6.0')] ).
cnf(207,plain,
equal(multiply(multiply(inverse(u),multiply(u,inverse(v))),inverse(inverse(v))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[120,16]),
[iquote('0:SpR:120.0,16.0')] ).
cnf(228,plain,
equal(multiply(inverse(u),inverse(inverse(u))),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[155,207,204]),
[iquote('0:Rew:155.0,207.0,204.0,207.0')] ).
cnf(234,plain,
equal(inverse(inverse(inverse(inverse(identity)))),inverse(identity)),
inference(spr,[status(thm),theory(equality)],[228,79]),
[iquote('0:SpR:228.0,79.0')] ).
cnf(236,plain,
equal(double_divide(inverse(identity),inverse(inverse(u))),inverse(inverse(inverse(u)))),
inference(spr,[status(thm),theory(equality)],[228,120]),
[iquote('0:SpR:228.0,120.0')] ).
cnf(242,plain,
equal(inverse(inverse(identity)),inverse(identity)),
inference(rew,[status(thm),theory(equality)],[133,234]),
[iquote('0:Rew:133.0,234.0')] ).
cnf(256,plain,
equal(double_divide(inverse(identity),inverse(identity)),identity),
inference(spr,[status(thm),theory(equality)],[242,4]),
[iquote('0:SpR:242.0,4.0')] ).
cnf(276,plain,
equal(inverse(identity),identity),
inference(rew,[status(thm),theory(equality)],[242,256,74]),
[iquote('0:Rew:242.0,256.0,74.0,256.0')] ).
cnf(289,plain,
equal(double_divide(double_divide(u,double_divide(double_divide(inverse(u),v),identity)),identity),v),
inference(rew,[status(thm),theory(equality)],[276,54]),
[iquote('0:Rew:276.0,54.0')] ).
cnf(296,plain,
equal(double_divide(double_divide(u,multiply(v,inverse(u))),identity),double_divide(identity,inverse(v))),
inference(rew,[status(thm),theory(equality)],[276,76]),
[iquote('0:Rew:276.0,76.0')] ).
cnf(314,plain,
equal(double_divide(identity,inverse(inverse(u))),inverse(inverse(inverse(u)))),
inference(rew,[status(thm),theory(equality)],[276,236]),
[iquote('0:Rew:276.0,236.0')] ).
cnf(356,plain,
equal(multiply(multiply(u,inverse(v)),v),u),
inference(rew,[status(thm),theory(equality)],[6,289,3]),
[iquote('0:Rew:6.0,289.0,3.0,289.0,6.0,289.0,3.0,289.0')] ).
cnf(364,plain,
equal(multiply(multiply(u,inverse(v)),v),double_divide(identity,inverse(u))),
inference(rew,[status(thm),theory(equality)],[6,296,3]),
[iquote('0:Rew:6.0,296.0,3.0,296.0')] ).
cnf(365,plain,
equal(double_divide(identity,inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[356,364]),
[iquote('0:Rew:356.0,364.0')] ).
cnf(367,plain,
equal(inverse(inverse(inverse(u))),inverse(u)),
inference(rew,[status(thm),theory(equality)],[365,314]),
[iquote('0:Rew:365.0,314.0')] ).
cnf(475,plain,
equal(double_divide(identity,inverse(u)),inverse(inverse(u))),
inference(spr,[status(thm),theory(equality)],[367,365]),
[iquote('0:SpR:367.0,365.0')] ).
cnf(484,plain,
equal(inverse(inverse(u)),u),
inference(rew,[status(thm),theory(equality)],[365,475]),
[iquote('0:Rew:365.0,475.0')] ).
cnf(485,plain,
$false,
inference(unc,[status(thm)],[484,14]),
[iquote('0:UnC:484.0,14.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GRP485-1 : TPTP v8.1.0. Released v2.6.0.
% 0.00/0.11 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon Jun 13 22:44:27 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.15/0.38
% 0.15/0.38 SPASS V 3.9
% 0.15/0.38 SPASS beiseite: Proof found.
% 0.15/0.38 % SZS status Theorem
% 0.15/0.38 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.38 SPASS derived 299 clauses, backtracked 0 clauses, performed 0 splits and kept 120 clauses.
% 0.15/0.38 SPASS allocated 63665 KBytes.
% 0.15/0.38 SPASS spent 0:00:00.06 on the problem.
% 0.15/0.38 0:00:00.02 for the input.
% 0.15/0.38 0:00:00.00 for the FLOTTER CNF translation.
% 0.15/0.38 0:00:00.00 for inferences.
% 0.15/0.38 0:00:00.00 for the backtracking.
% 0.15/0.38 0:00:00.02 for the reduction.
% 0.15/0.38
% 0.15/0.38
% 0.15/0.38 Here is a proof with depth 7, length 48 :
% 0.15/0.38 % SZS output start Refutation
% See solution above
% 0.15/0.38 Formulae used in the proof : single_axiom multiply inverse identity prove_these_axioms_2
% 0.15/0.38
%------------------------------------------------------------------------------